SOLUTION: The U.S. mint, which produces billions of coins annually, has a mean daily defect rate of 4 coins. Let X be the number of defective coins produced on a given day. On a given day

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Question 1020364: The U.S. mint, which produces billions of coins annually, has a mean daily defect rate of 4 coins. Let X be the number of defective coins produced on a given day.
On a given day, what is the probability of 3 or fewer defective coins
On a given day, what is the probability of more than 3 defective coins?
On a given day, what is the probability of exactly 4 defective coins
what is the variance?

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
This is an example of a rare event, so the Poisson distribution is the most appropriate to use.
p%28x%29+=+%28mu%5Ex%2Fx%21%29%2Ae%5E%28-mu%29
The mu in this case is equal to 4.
==>The probability of 3 or fewer defective coins would be p(0) +p(1) + p(2) + p(3) = , to 5 decimal places.
==> The probability of more than 3 defective coins is 1 - 0.43347 = 0.56653.
The probability of exactly 4 defectives is p%284%29+=++%284%5E4%2F4%21%29%2Ae%5E%28-4%29=0.19537, to 5 decimal places.
For the Poisson distribution, mu+=+sigma%5E2+=+4.